Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,6,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4167225929\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7081})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 1771x^{2} + 1770x + 3132900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(-20.7872 + 36.0044i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.6.k.e.109.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 32.7872 | − | 56.7890i | 0.586515 | − | 1.01587i | −0.408170 | − | 0.912906i | \(-0.633833\pi\) |
0.994685 | − | 0.102967i | \(-0.0328337\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 40.6487 | − | 123.104i | 0.313546 | − | 0.949573i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −122.787 | − | 212.674i | −0.305965 | − | 0.529946i | 0.671511 | − | 0.740995i | \(-0.265646\pi\) |
−0.977476 | + | 0.211048i | \(0.932312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 434.872 | 0.713679 | 0.356839 | − | 0.934166i | \(-0.383854\pi\) | ||||
0.356839 | + | 0.934166i | \(0.383854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −551.149 | − | 954.618i | −0.462537 | − | 0.801138i | 0.536550 | − | 0.843869i | \(-0.319727\pi\) |
−0.999087 | + | 0.0427312i | \(0.986394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1438.65 | − | 2491.81i | 0.914260 | − | 1.58355i | 0.106279 | − | 0.994336i | \(-0.466106\pi\) |
0.807981 | − | 0.589209i | \(-0.200560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2114.72 | + | 3662.80i | −0.833552 | + | 1.44375i | 0.0616521 | + | 0.998098i | \(0.480363\pi\) |
−0.895204 | + | 0.445657i | \(0.852970\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −587.497 | − | 1017.57i | −0.187999 | − | 0.325624i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4969.60 | −1.09730 | −0.548652 | − | 0.836051i | \(-0.684859\pi\) | ||||
−0.548652 | + | 0.836051i | \(0.684859\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4391.32 | + | 7606.00i | 0.820713 | + | 1.42152i | 0.905152 | + | 0.425088i | \(0.139757\pi\) |
−0.0844390 | + | 0.996429i | \(0.526910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5658.22 | − | 6344.64i | −0.780746 | − | 0.875462i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1220.03 | − | 2113.15i | 0.146510 | − | 0.253762i | −0.783425 | − | 0.621486i | \(-0.786529\pi\) |
0.929935 | + | 0.367723i | \(0.119863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3668.55 | 0.340828 | 0.170414 | − | 0.985373i | \(-0.445489\pi\) | ||||
0.170414 | + | 0.985373i | \(0.445489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7198.06 | −0.593669 | −0.296835 | − | 0.954929i | \(-0.595931\pi\) | ||||
−0.296835 | + | 0.954929i | \(0.595931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1636.66 | − | 2834.78i | 0.108072 | − | 0.187187i | −0.806917 | − | 0.590665i | \(-0.798866\pi\) |
0.914989 | + | 0.403478i | \(0.132199\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13502.4 | − | 10008.1i | −0.803378 | − | 0.595470i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1510.84 | − | 2616.84i | −0.0738801 | − | 0.127964i | 0.826719 | − | 0.562616i | \(-0.190205\pi\) |
−0.900599 | + | 0.434651i | \(0.856872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16103.4 | −0.717811 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25743.7 | − | 44589.5i | −0.962812 | − | 1.66764i | −0.715381 | − | 0.698735i | \(-0.753747\pi\) |
−0.247432 | − | 0.968905i | \(-0.579587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6656.65 | − | 11529.6i | 0.229050 | − | 0.396727i | −0.728477 | − | 0.685071i | \(-0.759771\pi\) |
0.957527 | + | 0.288344i | \(0.0931046\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14258.2 | − | 24695.9i | 0.418583 | − | 0.725007i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15447.9 | − | 26756.5i | −0.420418 | − | 0.728186i | 0.575562 | − | 0.817758i | \(-0.304783\pi\) |
−0.995980 | + | 0.0895723i | \(0.971450\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 41882.8 | 0.986030 | 0.493015 | − | 0.870021i | \(-0.335895\pi\) | ||||
0.493015 | + | 0.870021i | \(0.335895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17308.7 | − | 29979.5i | −0.380151 | − | 0.658441i | 0.610932 | − | 0.791683i | \(-0.290795\pi\) |
−0.991084 | + | 0.133242i | \(0.957461\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −31172.2 | + | 6470.74i | −0.599157 | + | 0.124373i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38771.7 | + | 67154.6i | −0.698952 | + | 1.21062i | 0.269878 | + | 0.962895i | \(0.413017\pi\) |
−0.968830 | + | 0.247726i | \(0.920317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −100908. | −1.60779 | −0.803897 | − | 0.594768i | \(-0.797244\pi\) | ||||
−0.803897 | + | 0.594768i | \(0.797244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72282.4 | −1.08514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 20391.8 | − | 35319.7i | 0.272886 | − | 0.472652i | −0.696714 | − | 0.717349i | \(-0.745355\pi\) |
0.969600 | + | 0.244697i | \(0.0786885\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17677.0 | − | 53534.6i | 0.223771 | − | 0.677690i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −94338.2 | − | 163399.i | −1.07245 | − | 1.85755i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 140147. | 1.51236 | 0.756178 | − | 0.654366i | \(-0.227064\pi\) | ||||
0.756178 | + | 0.654366i | \(0.227064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4288.23 | + | 7427.43i | 0.0418287 | + | 0.0724494i | 0.886182 | − | 0.463338i | \(-0.153348\pi\) |
−0.844353 | + | 0.535787i | \(0.820015\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17630.1 | − | 30536.2i | 0.163742 | − | 0.283610i | −0.772466 | − | 0.635057i | \(-0.780977\pi\) |
0.936208 | + | 0.351447i | \(0.114310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −96314.3 | + | 166821.i | −0.813264 | + | 1.40861i | 0.0973041 | + | 0.995255i | \(0.468978\pi\) |
−0.910568 | + | 0.413360i | \(0.864355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −61646.1 | − | 106774.i | −0.496980 | − | 0.860795i | 0.503014 | − | 0.864279i | \(-0.332225\pi\) |
−0.999994 | + | 0.00348322i | \(0.998891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −28400.9 | −0.209236 | −0.104618 | − | 0.994512i | \(-0.533362\pi\) | ||||
−0.104618 | + | 0.994512i | \(0.533362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 138671. | + | 240186.i | 0.977781 | + | 1.69357i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −139921. | + | 29044.9i | −0.905765 | + | 0.188019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 50372.1 | − | 87247.1i | 0.312771 | − | 0.541736i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 127870. | 0.731973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −47198.8 | −0.259670 | −0.129835 | − | 0.991536i | \(-0.541445\pi\) | ||||
−0.129835 | + | 0.991536i | \(0.541445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 39904.7 | − | 69116.9i | 0.203163 | − | 0.351889i | −0.746383 | − | 0.665517i | \(-0.768211\pi\) |
0.949546 | + | 0.313628i | \(0.101544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −248273. | − | 278392.i | −1.21703 | − | 1.36467i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −43032.1 | − | 74533.9i | −0.195881 | − | 0.339275i | 0.751308 | − | 0.659952i | \(-0.229423\pi\) |
−0.947189 | + | 0.320676i | \(0.896090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 270587. | 1.18787 | 0.593935 | − | 0.804513i | \(-0.297573\pi\) | ||||
0.593935 | + | 0.804513i | \(0.297573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −53396.7 | − | 92485.7i | −0.218360 | − | 0.378211i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −162939. | + | 282219.i | −0.643585 | + | 1.11472i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −86273.9 | + | 149431.i | −0.318356 | + | 0.551410i | −0.980145 | − | 0.198281i | \(-0.936464\pi\) |
0.661789 | + | 0.749690i | \(0.269798\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8949.75 | + | 15501.4i | 0.0319425 | + | 0.0553260i | 0.881555 | − | 0.472082i | \(-0.156497\pi\) |
−0.849612 | + | 0.527408i | \(0.823164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 575916. | 1.92544 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 89509.3 | + | 155035.i | 0.289814 | + | 0.501972i | 0.973765 | − | 0.227555i | \(-0.0730733\pi\) |
−0.683951 | + | 0.729528i | \(0.739740\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 364946. | + | 409219.i | 1.10959 | + | 1.24420i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 118645. | − | 205498.i | 0.349767 | − | 0.605814i | −0.636441 | − | 0.771325i | \(-0.719594\pi\) |
0.986208 | + | 0.165511i | \(0.0529275\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 94040.0 | 0.260928 | 0.130464 | − | 0.991453i | \(-0.458353\pi\) | ||||
0.130464 | + | 0.991453i | \(0.458353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −182180. | −0.490663 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 244357. | − | 423238.i | 0.620739 | − | 1.07515i | −0.368609 | − | 0.929584i | \(-0.620166\pi\) |
0.989348 | − | 0.145567i | \(-0.0465006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −149149. | + | 30960.4i | −0.368150 | + | 0.0764207i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 406498. | + | 704075.i | 0.948257 | + | 1.64243i | 0.749095 | + | 0.662462i | \(0.230488\pi\) |
0.199161 | + | 0.979967i | \(0.436178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −332961. | −0.755434 | −0.377717 | − | 0.925921i | \(-0.623291\pi\) | ||||
−0.377717 | + | 0.925921i | \(0.623291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −80002.7 | − | 138569.i | −0.171860 | − | 0.297671i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −135348. | + | 234430.i | −0.283040 | + | 0.490240i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −72143.9 | + | 124957.i | −0.143092 | + | 0.247843i | −0.928660 | − | 0.370933i | \(-0.879038\pi\) |
0.785567 | + | 0.618776i | \(0.212371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 447310. | + | 774763.i | 0.864400 | + | 1.49719i | 0.867641 | + | 0.497190i | \(0.165635\pi\) |
−0.00324119 | + | 0.999995i | \(0.501032\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 599462. | 1.10052 | 0.550258 | − | 0.834995i | \(-0.314530\pi\) | ||||
0.550258 | + | 0.834995i | \(0.314530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 389129. | + | 673992.i | 0.696564 | + | 1.20648i | 0.969651 | + | 0.244495i | \(0.0786222\pi\) |
−0.273086 | + | 0.961990i | \(0.588044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −202008. | + | 611780.i | −0.344055 | + | 1.04197i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 120282. | − | 208334.i | 0.199901 | − | 0.346238i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −706589. | −1.11893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −810532. | −1.25333 | −0.626663 | − | 0.779291i | \(-0.715580\pi\) | ||||
−0.626663 | + | 0.779291i | \(0.715580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −236004. | + | 408771.i | −0.348196 | + | 0.603093i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.11483e6 | − | 231418.i | 1.60717 | − | 0.333616i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −239679. | − | 415136.i | −0.330103 | − | 0.571755i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 220486. | 0.296905 | 0.148453 | − | 0.988920i | \(-0.452571\pi\) | ||||
0.148453 | + | 0.988920i | \(0.452571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 671890. | + | 1.16375e6i | 0.865433 | + | 1.49897i | 0.866617 | + | 0.498974i | \(0.166290\pi\) |
−0.00118391 | + | 0.999999i | \(0.500377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 521292. | − | 902904.i | 0.656889 | − | 1.13777i | −0.324528 | − | 0.945876i | \(-0.605205\pi\) |
0.981417 | − | 0.191889i | \(-0.0614614\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 316256. | − | 547771.i | 0.381635 | − | 0.661011i | −0.609661 | − | 0.792662i | \(-0.708694\pi\) |
0.991296 | + | 0.131651i | \(0.0420278\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −107323. | − | 185889.i | −0.126772 | − | 0.219575i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 684919. | 0.775612 | 0.387806 | − | 0.921741i | \(-0.373233\pi\) | ||||
0.387806 | + | 0.921741i | \(0.373233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3866.44 | + | 6696.87i | 0.00428814 | + | 0.00742728i | 0.868162 | − | 0.496282i | \(-0.165302\pi\) |
−0.863873 | + | 0.503709i | \(0.831968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.01105e6 | + | 438651.i | −1.07611 | + | 0.466878i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 625626. | − | 1.08362e6i | 0.652488 | − | 1.13014i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.09614e6 | −1.09820 | −0.549098 | − | 0.835758i | \(-0.685029\pi\) | ||||
−0.549098 | + | 0.835758i | \(0.685029\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03864e6 | 1.02015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 357460. | − | 619139.i | 0.337594 | − | 0.584730i | −0.646386 | − | 0.763011i | \(-0.723720\pi\) |
0.983980 | + | 0.178281i | \(0.0570536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −210546. | − | 236088.i | −0.195028 | − | 0.218688i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −298256. | − | 516595.i | −0.265889 | − | 0.460533i | 0.701907 | − | 0.712268i | \(-0.252332\pi\) |
−0.967796 | + | 0.251735i | \(0.918999\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −198144. | −0.173327 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.01654e6 | − | 1.76070e6i | −0.856531 | − | 1.48356i | −0.875217 | − | 0.483730i | \(-0.839282\pi\) |
0.0186864 | − | 0.999825i | \(-0.494052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −897277. | + | 1.55413e6i | −0.742170 | + | 1.28548i | 0.209336 | + | 0.977844i | \(0.432870\pi\) |
−0.951505 | + | 0.307632i | \(0.900463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −144274. | + | 249890.i | −0.115042 | + | 0.199259i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −211790. | − | 366831.i | −0.165846 | − | 0.287254i | 0.771109 | − | 0.636703i | \(-0.219702\pi\) |
−0.936956 | + | 0.349449i | \(0.886369\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.63799e6 | 1.23750 | 0.618749 | − | 0.785589i | \(-0.287640\pi\) | ||||
0.618749 | + | 0.785589i | \(0.287640\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 147018. | + | 254642.i | 0.109120 | + | 0.189001i | 0.915414 | − | 0.402514i | \(-0.131863\pi\) |
−0.806294 | + | 0.591515i | \(0.798530\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 149122. | − | 451615.i | 0.106865 | − | 0.323641i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 102399. | − | 177360.i | 0.0721191 | − | 0.124914i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 356961. | 0.242913 | 0.121457 | − | 0.992597i | \(-0.461243\pi\) | ||||
0.121457 | + | 0.992597i | \(0.461243\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.37626e6 | −2.25881 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −919631. | + | 1.59285e6i | −0.594888 | + | 1.03038i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −292592. | + | 886113.i | −0.186143 | + | 0.563732i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −436505. | − | 756049.i | −0.268683 | − | 0.465372i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.04097e6 | −1.23592 | −0.617960 | − | 0.786210i | \(-0.712041\pi\) | ||||
−0.617960 | + | 0.786210i | \(0.712041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.02337e6 | + | 1.77253e6i | 0.599972 | + | 1.03918i | 0.992824 | + | 0.119581i | \(0.0381552\pi\) |
−0.392852 | + | 0.919602i | \(0.628512\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −319272. | + | 552996.i | −0.184205 | + | 0.319052i | −0.943308 | − | 0.331918i | \(-0.892304\pi\) |
0.759104 | + | 0.650970i | \(0.225638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.74954e6 | − | 3.03030e6i | 0.977860 | − | 1.69370i | 0.307705 | − | 0.951482i | \(-0.400439\pi\) |
0.670155 | − | 0.742221i | \(-0.266228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 610203. | + | 1.05690e6i | 0.335736 | + | 0.581512i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.17163e6 | −1.69152 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −255486. | − | 442514.i | −0.134171 | − | 0.232391i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −282446. | − | 316710.i | −0.143862 | − | 0.161314i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.47089e6 | − | 2.54766e6i | 0.737923 | − | 1.27812i | −0.215506 | − | 0.976503i | \(-0.569140\pi\) |
0.953429 | − | 0.301618i | \(-0.0975266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.02597e6 | −0.986326 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.77854e6 | 1.33273 | 0.666364 | − | 0.745627i | \(-0.267850\pi\) | ||||
0.666364 | + | 0.745627i | \(0.267850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.07840e6 | − | 1.86784e6i | 0.502218 | − | 0.869868i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.78089e6 | + | 1.25539e6i | −0.817338 | + | 0.576159i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −86001.9 | − | 148960.i | −0.0383429 | − | 0.0664118i | 0.846217 | − | 0.532838i | \(-0.178875\pi\) |
−0.884560 | + | 0.466426i | \(0.845541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.88321e6 | −1.70658 | −0.853290 | − | 0.521436i | \(-0.825397\pi\) | ||||
−0.853290 | + | 0.521436i | \(0.825397\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −385467. | − | 667649.i | −0.164646 | − | 0.285175i | 0.771884 | − | 0.635764i | \(-0.219315\pi\) |
−0.936529 | + | 0.350589i | \(0.885981\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.37322e6 | − | 2.37849e6i | 0.578321 | − | 1.00168i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.57017e6 | − | 2.71961e6i | 0.642998 | − | 1.11370i | −0.341763 | − | 0.939786i | \(-0.611024\pi\) |
0.984760 | − | 0.173918i | \(-0.0556428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.90135e6 | − | 5.02529e6i | −1.17174 | − | 2.02952i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.27001e6 | −0.891857 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 182842. | + | 316691.i | 0.0708615 | + | 0.122736i | 0.899279 | − | 0.437375i | \(-0.144092\pi\) |
−0.828418 | + | 0.560111i | \(0.810758\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −383559. | + | 79619.2i | −0.144676 | + | 0.0300319i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 77129.9 | − | 133593.i | 0.0287045 | − | 0.0497177i | −0.851316 | − | 0.524653i | \(-0.824195\pi\) |
0.880021 | + | 0.474935i | \(0.157528\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.16114e6 | −0.783122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.06013e6 | 1.45192 | 0.725959 | − | 0.687738i | \(-0.241396\pi\) | ||||
0.725959 | + | 0.687738i | \(0.241396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.02152e6 | − | 1.76932e6i | 0.355834 | − | 0.616323i | −0.631426 | − | 0.775436i | \(-0.717530\pi\) |
0.987260 | + | 0.159113i | \(0.0508633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −654581. | + | 1.98240e6i | −0.225067 | + | 0.681614i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.06183e6 | − | 1.83915e6i | −0.355780 | − | 0.616229i | 0.631471 | − | 0.775399i | \(-0.282451\pi\) |
−0.987251 | + | 0.159170i | \(0.949118\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.66209e6 | 1.54219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.54243e6 | + | 4.40362e6i | 0.819892 | + | 1.42009i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.83182e6 | − | 3.17280e6i | 0.583319 | − | 1.01034i | −0.411764 | − | 0.911291i | \(-0.635087\pi\) |
0.995083 | − | 0.0990473i | \(-0.0315795\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32044.9 | + | 55503.3i | −0.00995170 | + | 0.0172369i | −0.870958 | − | 0.491357i | \(-0.836501\pi\) |
0.861007 | + | 0.508594i | \(0.169834\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90966e6 | + | 3.30763e6i | 0.585725 | + | 1.01451i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −599216. | −0.179307 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.01287e6 | − | 1.75434e6i | −0.299395 | − | 0.518568i | 0.676603 | − | 0.736348i | \(-0.263452\pi\) |
−0.975998 | + | 0.217781i | \(0.930118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.53561e6 | + | 1.35666e6i | −1.88543 | + | 0.391379i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.30849e6 | + | 5.73047e6i | −0.942995 | + | 1.63332i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.38986e6 | −0.665025 | −0.332513 | − | 0.943099i | \(-0.607896\pi\) | ||||
−0.332513 | + | 0.943099i | \(0.607896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46875e6 | 0.953822 | 0.476911 | − | 0.878952i | \(-0.341756\pi\) | ||||
0.476911 | + | 0.878952i | \(0.341756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −647596. | + | 1.12167e6i | −0.173913 | + | 0.301226i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.14877e6 | − | 1.28813e6i | −0.304903 | − | 0.341892i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −802201. | − | 1.38945e6i | −0.208013 | − | 0.360289i | 0.743076 | − | 0.669207i | \(-0.233366\pi\) |
−0.951088 | + | 0.308919i | \(0.900033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 741661. | 0.190102 | 0.0950508 | − | 0.995472i | \(-0.469699\pi\) | ||||
0.0950508 | + | 0.995472i | \(0.469699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.08466e6 | + | 1.05389e7i | 1.52417 | + | 2.63993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.43394e6 | + | 2.48365e6i | −0.355115 | + | 0.615077i | −0.987138 | − | 0.159873i | \(-0.948892\pi\) |
0.632023 | + | 0.774950i | \(0.282225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −89148.9 | + | 154410.i | −0.0215827 | + | 0.0373824i | −0.876615 | − | 0.481192i | \(-0.840204\pi\) |
0.855032 | + | 0.518575i | \(0.173537\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.33718e6 | − | 2.31607e6i | −0.320103 | − | 0.554435i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.77890e6 | 0.650515 | 0.325258 | − | 0.945625i | \(-0.394549\pi\) | ||||
0.325258 | + | 0.945625i | \(0.394549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −450451. | − | 780205.i | −0.104281 | − | 0.180621i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.46060e6 | − | 2.75911e6i | −0.557202 | − | 0.624798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.20669e6 | + | 5.55416e6i | −0.718236 | + | 1.24402i | 0.243462 | + | 0.969910i | \(0.421717\pi\) |
−0.961698 | + | 0.274111i | \(0.911617\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.88393e6 | 1.50864 | 0.754318 | − | 0.656510i | \(-0.227968\pi\) | ||||
0.754318 | + | 0.656510i | \(0.227968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.70530e6 | 1.45367 | 0.726835 | − | 0.686812i | \(-0.240991\pi\) | ||||
0.726835 | + | 0.686812i | \(0.240991\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.62836e6 | + | 2.82041e6i | −0.345509 | + | 0.598439i | −0.985446 | − | 0.169988i | \(-0.945627\pi\) |
0.639937 | + | 0.768427i | \(0.278960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.92178e6 | + | 814084.i | −0.823286 | + | 0.170898i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 883830. | + | 1.53084e6i | 0.181642 | + | 0.314613i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.38080e6 | −0.687520 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.67916e6 | + | 8.10454e6i | 0.931814 | + | 1.61395i | 0.780219 | + | 0.625506i | \(0.215108\pi\) |
0.151595 | + | 0.988443i | \(0.451559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 530557. | − | 918951.i | 0.104561 | − | 0.181105i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.59502e6 | − | 7.95881e6i | 0.887019 | − | 1.53636i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.31470e6 | + | 2.27712e6i | 0.251191 | + | 0.435075i | 0.963854 | − | 0.266431i | \(-0.0858445\pi\) |
−0.712663 | + | 0.701506i | \(0.752511\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.81856e6 | 0.902015 | 0.451008 | − | 0.892520i | \(-0.351065\pi\) | ||||
0.451008 | + | 0.892520i | \(0.351065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.73899e6 | + | 4.74407e6i | 0.507543 | + | 0.879091i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.70248e6 | − | 5.15596e6i | 0.309166 | − | 0.936308i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.09549e6 | − | 3.62949e6i | 0.376733 | − | 0.652521i | −0.613851 | − | 0.789422i | \(-0.710381\pi\) |
0.990585 | + | 0.136900i | \(0.0437139\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.75338e6 | 0.308999 | 0.154500 | − | 0.987993i | \(-0.450623\pi\) | ||||
0.154500 | + | 0.987993i | \(0.450623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 562395. | 0.0981326 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.80923e6 | − | 4.86573e6i | 0.480610 | − | 0.832441i | −0.519142 | − | 0.854688i | \(-0.673749\pi\) |
0.999753 | + | 0.0222464i | \(0.00708185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.39418e6 | + | 912146.i | −0.744433 | + | 0.154530i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.15608e6 | − | 2.00239e6i | −0.192075 | − | 0.332683i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −803844. | −0.132265 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.53589e6 | + | 9.58845e6i | 0.893498 | + | 1.54758i | 0.835653 | + | 0.549258i | \(0.185089\pi\) |
0.0578446 | + | 0.998326i | \(0.481577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.79894e6 | − | 6.57996e6i | 0.607307 | − | 1.05189i | −0.384375 | − | 0.923177i | \(-0.625583\pi\) |
0.991682 | − | 0.128710i | \(-0.0410836\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.84055e6 | − | 8.38407e6i | 0.759220 | − | 1.31501i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.72588e6 | − | 9.91752e6i | −0.889618 | − | 1.54086i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.59535e6 | 0.243242 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.31575e6 | + | 1.09392e7i | 0.953982 | + | 1.65235i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −470532. | + | 4.10046e6i | −0.0697618 | + | 0.607940i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.67539e6 | − | 2.90187e6i | 0.246107 | − | 0.426270i | −0.716335 | − | 0.697756i | \(-0.754182\pi\) |
0.962442 | + | 0.271486i | \(0.0875152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.08480e6 | −1.16595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00856e7 | −1.44123 | −0.720615 | − | 0.693335i | \(-0.756140\pi\) | ||||
−0.720615 | + | 0.693335i | \(0.756140\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.14950e6 | + | 1.23833e7i | −1.00322 | + | 1.73763i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.69101e6 | + | 7.50272e6i | 0.930419 | + | 1.04329i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.78337e6 | + | 1.17491e7i | 0.926419 | + | 1.60460i | 0.789263 | + | 0.614055i | \(0.210463\pi\) |
0.137155 | + | 0.990550i | \(0.456204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.13023e6 | −0.423689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.98494e6 | − | 3.43802e6i | −0.263922 | − | 0.457127i | 0.703358 | − | 0.710835i | \(-0.251683\pi\) |
−0.967281 | + | 0.253708i | \(0.918350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −931185. | + | 1.61286e6i | −0.122720 | + | 0.212557i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.08724e6 | + | 3.61521e6i | −0.270267 | + | 0.468116i | −0.968930 | − | 0.247335i | \(-0.920445\pi\) |
0.698663 | + | 0.715451i | \(0.253779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.92833e6 | − | 3.33996e6i | −0.247509 | − | 0.428698i | 0.715325 | − | 0.698792i | \(-0.246279\pi\) |
−0.962834 | + | 0.270094i | \(0.912945\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.96956e6 | 0.626828 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.12288e6 | + | 1.94488e6i | 0.140408 | + | 0.243194i | 0.927650 | − | 0.373450i | \(-0.121825\pi\) |
−0.787242 | + | 0.616644i | \(0.788492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.10178e6 | + | 1.24222e7i | −0.504118 | + | 1.52672i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −371023. | + | 642630.i | −0.0452094 | + | 0.0783050i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.40082e6 | −0.766726 | −0.383363 | − | 0.923598i | \(-0.625234\pi\) | ||||
−0.383363 | + | 0.923598i | \(0.625234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.52702e7 | 3.00138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.56031e6 | − | 9.63074e6i | 0.649325 | − | 1.12466i | −0.333959 | − | 0.942588i | \(-0.608385\pi\) |
0.983284 | − | 0.182077i | \(-0.0582820\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.93818e6 | + | 8.89828e6i | −0.340241 | + | 1.03042i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.56707e6 | − | 1.13745e7i | −0.747833 | − | 1.29528i | −0.948860 | − | 0.315698i | \(-0.897761\pi\) |
0.201027 | − | 0.979586i | \(-0.435572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.88546e6 | −0.890514 | −0.445257 | − | 0.895403i | \(-0.646888\pi\) | ||||
−0.445257 | + | 0.895403i | \(0.646888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.30312e6 | − | 5.72117e6i | −0.366890 | − | 0.635472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.82967e6 | − | 6.63319e6i | 0.421881 | − | 0.730719i | −0.574243 | − | 0.818685i | \(-0.694703\pi\) |
0.996123 | + | 0.0879660i | \(0.0280367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 711738. | − | 1.23277e6i | 0.0771289 | − | 0.133591i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.62066e6 | + | 1.31994e7i | 0.819108 | + | 1.41874i | 0.906340 | + | 0.422549i | \(0.138864\pi\) |
−0.0872322 | + | 0.996188i | \(0.527802\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.35844e7 | −1.43657 | −0.718285 | − | 0.695749i | \(-0.755073\pi\) | ||||
−0.718285 | + | 0.695749i | \(0.755073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.18709e6 | − | 5.52019e6i | −0.334324 | − | 0.579066i | 0.649031 | − | 0.760762i | \(-0.275175\pi\) |
−0.983355 | + | 0.181696i | \(0.941841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.51911e6 | − | 3.94602e6i | −0.363256 | − | 0.407323i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.02844e6 | − | 1.04416e7i | 0.617312 | − | 1.06922i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.68967e6 | −0.271065 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.42736e7 | −1.42712 | −0.713561 | − | 0.700593i | \(-0.752919\pi\) | ||||
−0.713561 | + | 0.700593i | \(0.752919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.54751e6 | + | 2.68037e6i | −0.152300 | + | 0.263792i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.87180e6 | − | 4.35222e6i | −0.573354 | − | 0.424974i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.63480e6 | − | 8.02771e6i | −0.445539 | − | 0.771697i | 0.552550 | − | 0.833480i | \(-0.313655\pi\) |
−0.998090 | + | 0.0617828i | \(0.980321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.17375e7 | 1.11956 | 0.559780 | − | 0.828641i | \(-0.310885\pi\) | ||||
0.559780 | + | 0.828641i | \(0.310885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.12724e6 | + | 8.88063e6i | 0.481529 | + | 0.834033i | 0.999775 | − | 0.0211984i | \(-0.00674818\pi\) |
−0.518246 | + | 0.855232i | \(0.673415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.32200e6 | + | 1.09500e7i | −0.589173 | + | 1.02048i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.14489e6 | − | 7.17915e6i | 0.380391 | − | 0.658856i | −0.610727 | − | 0.791841i | \(-0.709123\pi\) |
0.991118 | + | 0.132985i | \(0.0424562\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.61672e6 | − | 4.53230e6i | −0.238317 | − | 0.412776i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.06731e7 | 1.85435 | 0.927174 | − | 0.374631i | \(-0.122230\pi\) | ||||
0.927174 | + | 0.374631i | \(0.122230\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −97171.2 | − | 168305.i | −0.00865035 | − | 0.0149829i | 0.861668 | − | 0.507473i | \(-0.169420\pi\) |
−0.870318 | + | 0.492490i | \(0.836087\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.39498e7 | + | 4.97151e6i | −2.10014 | + | 0.435948i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.05093e7 | − | 1.82026e7i | 0.914659 | − | 1.58424i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.26940e6 | −0.280325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.14437e7 | −0.973929 | −0.486965 | − | 0.873422i | \(-0.661896\pi\) | ||||
−0.486965 | + | 0.873422i | \(0.661896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.51869e6 | − | 7.82660e6i | 0.378914 | − | 0.656299i | −0.611990 | − | 0.790865i | \(-0.709631\pi\) |
0.990905 | + | 0.134567i | \(0.0429642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.69679e6 | − | 1.72527e7i | 0.474193 | − | 1.43609i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.59212e6 | − | 9.68584e6i | −0.458696 | − | 0.794485i | 0.540196 | − | 0.841539i | \(-0.318350\pi\) |
−0.998892 | + | 0.0470541i | \(0.985017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.64361e6 | −0.459548 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −657020. | − | 1.13799e6i | −0.0527267 | − | 0.0913253i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.83465e6 | + | 4.90976e6i | −0.225842 | + | 0.391170i | −0.956572 | − | 0.291497i | \(-0.905847\pi\) |
0.730730 | + | 0.682667i | \(0.239180\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.87177e6 | − | 1.53664e7i | 0.696704 | − | 1.20673i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.02192e6 | − | 3.50207e6i | −0.157646 | − | 0.273050i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.31822e6 | 0.101320 | 0.0506599 | − | 0.998716i | \(-0.483868\pi\) | ||||
0.0506599 | + | 0.998716i | \(0.483868\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.51038e6 | − | 6.08016e6i | −0.267896 | − | 0.464009i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.08866e6 | − | 225984.i | 0.0819112 | − | 0.0170032i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.13018e6 | + | 7.15368e6i | −0.308570 | + | 0.534458i | −0.978050 | − | 0.208372i | \(-0.933184\pi\) |
0.669480 | + | 0.742830i | \(0.266517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.71456e7 | −2.73643 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.00290e6 | −0.512287 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.13372e7 | − | 1.96365e7i | 0.817865 | − | 1.41658i | −0.0893870 | − | 0.995997i | \(-0.528491\pi\) |
0.907252 | − | 0.420587i | \(-0.138176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.04250e6 | − | 3.41159e6i | −0.217968 | − | 0.244410i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.91963e6 | + | 5.05694e6i | 0.206292 | + | 0.357308i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.93477e7 | −1.35767 | −0.678833 | − | 0.734293i | \(-0.737514\pi\) | ||||
−0.678833 | + | 0.734293i | \(0.737514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.96720e6 | + | 6.87140e6i | 0.274594 | + | 0.475611i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.42922e6 | + | 1.28678e7i | −0.510720 | + | 0.884593i | 0.489203 | + | 0.872170i | \(0.337288\pi\) |
−0.999923 | + | 0.0124232i | \(0.996045\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.79360e6 | + | 6.57071e6i | −0.257266 | + | 0.445598i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.84089e6 | + | 1.53129e7i | 0.595504 | + | 1.03144i | 0.993476 | + | 0.114045i | \(0.0363810\pi\) |
−0.397971 | + | 0.917398i | \(0.630286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.28756e6 | 0.550750 | 0.275375 | − | 0.961337i | \(-0.411198\pi\) | ||||
0.275375 | + | 0.961337i | \(0.411198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.65735e6 | + | 9.79882e6i | 0.373442 | + | 0.646820i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.66214e7 | + | 1.86378e7i | 1.08259 | + | 1.21392i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15682e7 | − | 2.00368e7i | 0.748457 | − | 1.29637i | −0.200104 | − | 0.979775i | \(-0.564128\pi\) |
0.948562 | − | 0.316592i | \(-0.102539\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.17375e6 | 0.0749389 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.95475e7 | −1.23980 | −0.619900 | − | 0.784681i | \(-0.712827\pi\) | ||||
−0.619900 | + | 0.784681i | \(0.712827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.91233e6 | − | 6.77635e6i | 0.244891 | − | 0.424164i | −0.717210 | − | 0.696857i | \(-0.754581\pi\) |
0.962101 | + | 0.272693i | \(0.0879144\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.56502e7 | + | 3.24867e6i | −0.973214 | + | 0.202020i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.11952e7 | − | 1.93907e7i | −0.687139 | − | 1.19016i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.27325e6 | −0.504499 | −0.252250 | − | 0.967662i | \(-0.581170\pi\) | ||||
−0.252250 | + | 0.967662i | \(0.581170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.41844e6 | − | 1.63132e7i | −0.566931 | − | 0.981953i | −0.996867 | − | 0.0790941i | \(-0.974797\pi\) |
0.429936 | − | 0.902859i | \(-0.358536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.15978e6 | − | 8.93700e6i | 0.308587 | − | 0.534488i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.27775e6 | − | 9.14133e6i | 0.311605 | − | 0.539717i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.14267e6 | − | 8.90737e6i | −0.301690 | − | 0.522543i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.17390e7 | 0.679920 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.19734e6 | + | 1.59303e7i | 0.529329 | + | 0.916824i | 0.999415 | + | 0.0342037i | \(0.0108895\pi\) |
−0.470086 | + | 0.882621i | \(0.655777\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 |